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CFA Level I · CFA Level I Exam · Valuing a Derivative Using a One-Period Binomial Model

In a one-period binomial model, an analyst builds a portfolio of the underlying asset and a risk-free bond that reproduces the payoffs of a call option in both the up and down states. The portfolio most likely has a value today that equals:

The replicating portfolio's value today equals the option's no-arbitrage price. Because the portfolio matches the option's payoff in both the up and down states, any other price would allow arbitrage profits, so the cost of building the portfolio gives the option's fair value.

  1. Athe call option's expected payoff in the up state
  2. Bthe no-arbitrage price of the call optionCorrect
  3. Cthe underlying price minus the option's exercise price

Explanation

A replicating portfolio has the same payoffs as the option in every state. To avoid arbitrage, the portfolio and the option must have the same value today. The other options ignore discounting and probabilities, or use intrinsic value that omits time value.

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